WordPress is now officially starting to support SQLite as documented here. It's still in early testing. It means all we'll need in future is a web server with PHP to run WordPress.
With the fact that it will no longer require a MySQL database server, I thought it would be good to get this onto the roadmap. I'm more concerned about the 'management side', i.e. using for example Adminer or phpLiteAdmin to manage the databases.
Once this has been fully supported by WordPress, I will be using SQLite in favor of a database server. In the meantime, I intend to test their integration on a smaller subset of 'basic' WordPress websites and use phpLiteAdmin to manage the databases whenever needed.